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Prove that route 5 is irrational |
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Answer» Hence, ROOT 5 is irrational ?????? Let√ 2 be a rational numberTherefore,√2 =a/bWhere a & b are Co-prime integers &b is not = 0Therefore,a/b=√2a= √2bSquaring both sides (a)2=(√2b)2a2= 2b2......(1)This implies 2 divides a2So,2 ➗ aSo let a = 2 c for some integerPut this in (1...)(2c)2 = 2b square4c square= 2b square2c square= b squareThis implies, 2 divides b squareSo,2 divides bTherefor, a & have 2 as commen factor but this contradicts that a & b no common factor then b. Therefore our aaaumption is wrongHence √2 is irrationalThis is the method of doing question you just have to change it from √ 2 to √5 and all over method is same.. Let us assume that √5 is a rational number.we know that the rational numbers are in the form of p/q form where p,q are integers.so, √5 = p/q p = √5qwe know that \'p\' is a rational number. so √5 q must be rational since it equals to pbut it doesn\'t occurs with √5 since its not an integertherefore, p = √5qthis contradicts the fact that √5 is an irrational numberhence our assumption is wrong and √5 is an irrational number.\xa0 This app is for aking homework related questions. And he is doing ✔ This app is for chatting olny Ask to your teacher don\'t ask this type of questions in this app |
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